Use Cylindrical or Spherical Coordinates, Whichever Seems More Appropriate, to Evaluate

question 23

Multiple Choice

Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate $\iiint _ { E } z d V$ where $E$ lies above the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ and below the plane $z = 16$ .

• A) \(- 160.28\)
• B) \(176.38\)
• C) \(4,289.32\)
• D) \(175.93\)
• E) \(175.37\)

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Definitions:

Perkins

Depending on the context, Perkins could refer to a person's last name, but in educational or cognitive theory contexts, it might relate to David Perkins, an educational theorist known for his work on intelligence and creativity.

Large Knowledge Base

A comprehensive collection of information, facts, and rules used in decision-making processes or computational systems.

Essential Structure

The fundamental or intrinsic architecture of an entity or concept, which determines its nature and characteristics.

Parallelogram

A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length, and opposite angles that are equal.